a) Field of the Invention
The present invention relates to a soft X-ray microscope which is to be used for observing and measuring objects by utilizing soft X-rays having wavelengths within a range from several angstroms to several hundred angstroms.
b) Description of the Prior Art
The type of light sources for the conventional optical microscopes are halogen lamps, xenon lamps, mercury lamps and the like, which have light emitting members of finite sizes and emit incoherent rays diverging in all directions in space. Therefore, these light sources are generally used for illumination in Kohler mode since illumination in this mode can easily be performed by projecting an image of a light source 1 to a location at an infinite distance by a condenser 2 for illuminating a sample 3 as illustrated in FIG. 1.
The type of radiation sources for soft X-ray microscopes are X-ray sources of the conventional type which an electron beam, laser plasma radiation sources which utilize high-output pulse lasers developed one after another in the recent years and synchrotron radiation sources. Though the X-ray radiation sources of the type which an electron beam and the plasma radiation sources have radiation emitting members of finite sizes, they can hardly be used for illumination in the Kohler mode since the radiation sources use radiation emitting members which are very small (several microns to several hundred microns). Accordingly, the X-ray radiation sources are used generally for illumination in a critical mode wherein an image of a radiation source 4 is projected onto a sample 3 by using a condenser 2 as illustrated in FIG. 2. In the region of the soft X-rays, however, a zone plate utilizing diffraction or a reflecting mirror is used as the condenser. The radiation sources having radiation emitting members which are small but have directivities are usable for illumination in the Kohler mode (diverging in space), are actually used for illumination in the critical mode.
FIG. 3 illustrates a fundamental optical system for microscopes. In this drawing, the reference numeral 1 represents a radiation source, the reference numeral 2 designates a condenser, the reference numeral 3 denotes a sample, the reference numeral 6 represents an objective optical system and the reference numeral 7 designates an image surface. The optical system for microscopes illustrated in FIG. 3 can generally be regarded as a partially coherent optical system which has an imaging characteristic given in a form subjected to Fourier transformation as expressed by the formula (1) shown below (see Kogaku Gijutsu Handbook, p 118 and later, Asakura Shoten, Kogaku No Genri III, p 781 and later, Tokai Daigaku Shuppankai, etc.): ##EQU1## wherein the reference symbol I(x,y) represents brightness of image, the reference symbols x and y designate coordinates on an image surface, the reference symbols m, n, p and q denote spatial frequencies, the reference symbol j represents the imaginary unit, the reference symbol T designates transmittance distribution t of the sample subjected to Fourier transformation, the reference symbol T* denotes a complex conjugation of T and C(m,n;p,q) represents a transfer function of the partially coherent optical system expressed by the following formula (2): ##EQU2## wherein the reference symbol p.sub.1 (u,v) represents a pupil function of the objective optical system, the reference symbol p.sub.2 (u,v) designates a pupil function of the condenser, the reference symbols u and v denote coordinates on the pupil surface, m is equal to .lambda.fm expressed by using wavelength .lambda. of radiation and the reference symbol f represents a focal length of the objective optical system.
The formula (1) mentioned above means that Fourier transformation is performed by multiplying the transmittance distribution t of the sample subjected to the Fourier transformation, i.e., a spatial frequency spectrum of the sample by C(m,n;p,q) which represents a frequency characteristic of a transfer function of the optical system. This means that a spot image response function of the optical system and an amplitude transmittance distribution of the sample are convoluted in real space.
The formula (2) mentioned above means that the transfer function C(m,n;p,q) is obtained by correlating the pupil function P.sub.2 of the condenser to the pupil function p.sub.1.
Let us consider the frequency characteristic of the optical system only in one direction for simplicity of description which will be made below for pointing out problems of microscopes using the radiation sources. When considered only in one direction, the formula (2) mentioned above gives a transfer function expressed by the following formula (3): ##EQU3## Let us assume that contrast is low on the sample or that a radiation bundle coming from the sample is scarcely scattered. It is already known that transmission of an image can be discussed in this case while considering a transfer function of C(m,o) (see, for example, Philos. Trans. R. Soc. London, A295 (1415) pp. 513 (1980)). In this case the formula (3) can be transformed as follows: ##EQU4## Though the formula (4) has an integration range of -.infin. to +.infin., this range is determined dependently on sizes of the optical system and the condenser since the pupil function has no value outside a range of a pupil. When the objective optical system has a pupil of a size traced as a circle in FIG. 4, the formula (4) has a value which corresponds to an area which is slashed in FIG. 4.
In case of an ordinary optical microscope, a light source has a large size 7 and a diameter of a light bundle to be allowed to be incident on the optical system thereof is determined dependently on an aperture of an aperture stop disposed before the condenser. The aperture of the aperture stop is ordinarily adjusted in conjunction with a numerical aperture of the objective optical system comprised in the microscope. Therefore, the light source is used for illumination in an incoherent mode, but the size of the condenser is equal to that of the pupil of the optical system in this case and let us represents a radius of these pupils by a reference symbol a.sub.1. When the transfer function C(m,n) is traced on coordinates taking the spatial frequency as the abscissa, we obtain a curve A shown in FIG. 5. In this case, we obtain a cutoff frequency expressed as follows: EQU 2a.sub.1 /(.lambda.f) (=2NA/.lambda.)
wherein the reference symbol NA represents a numerical aperture.
Further, size of the aperture of the aperture stop disposed before the condenser is often adjusted to 0.8 to 0.9 times as large as the numerical aperture of the objective optical system when contrast is low on the sample. This adjustment is performed for emphasizing locations at which the sample varies phases thereof by enhancing a degree of coherence of the illumination system and for facilitating observation of the sample by enhancing image contrast. In this case, the transfer function C(m,n) is represented by the curve B shown in FIG. 5 and the cutoff frequency is expressed as follows: EQU (a.sub.1 +a.sub.2)/(.lambda.f)
wherein the reference symbol a.sub.1 represents a radius of the pupil of the objective optical system and the reference symbol a.sub.2 designates a radius of the pupil of the condenser. In this case, it is difficult to quantitatively judge whether the image contrast represents variation of transmittance or phase of the sample.
Now, let us consider a case wherein the aperture of the aperture stop disposed before the condenser is extremely small. In this case, the radiation source is used as a spot source for illumination with a radiation. In this case, illumination is performed in a coherent mode and the transfer function C(m,n) is as represented by the curve C shown in FIG. 5. Then, the cutoff frequency is a.sub.1 /(.lambda.f) and has a value equal to half the value obtained by the incoherent illumination. Further, the degree of coherence of the illumination system becomes extremely high, whereby it is impossible to judge whether an image represents the variation of transmittance or the variation of phase.
When a microscope uses a radiation source or a coherent illumination system as described above, an image has high contrast but does not permit a microscopist to interpret the meaning of the image. In addition, such a radiation source poses a problem in that the resolving power of the microscope combined with the radiation source is lowered to approximately 50%. This problem has never been discussed by the prior art of which taught that light sources having light emitting members of finite sizes were to be used for microscopes.
Moreover, the point radiation sources such as the laser plasma radiation sources are used inevitably for illumination in the critical mode since these radiation sources cannot be effectively used for Kohler illumination. These radiation source provide illumination in an incoherent mode wherein the cutoff frequency is as represented by the curve A or B, but the critical illumination is problematic in that luminance distributions on radiation sources appear directly as illumination distributions on images.